Question

ABCD is a rectangle and P is the midpoint of intersection of diagonals. If angle BPC=124° , find angle BAP :

Answer 1

We know a rectangle is a parallelogram since it's opposite sides are equal and parallel to each other.
Thus we know a parallelogram has equal diagonals and both the diagonals bisect each other. -- (1)
Thus now we know that BP=BC
Thus ∆BPC is an isosceles triangle .
Thus B°=C°(Let B=C=x)
We know that in a triangle , sum of all angles of equal to 180°
Therefore ATP ,
124+2x=180
=>2x=56
=>x=28
B°=(PBC)°+(PBA°)
90°=28°+(PBA)°
(PBA)°=62°
Using the same theory as (1)
BAP is also equal to PBA
Thus BAP=62°
HOPE IT HELPS